Path: ...!weretis.net!feeder9.news.weretis.net!feeder8.news.weretis.net!eternal-september.org!feeder3.eternal-september.org!news.eternal-september.org!.POSTED!not-for-mail From: Mikko Newsgroups: sci.logic Subject: Re: True on the basis of meaning --- Good job Richard ! ---Socratic method (agreement) Date: Wed, 22 May 2024 10:57:12 +0300 Organization: - Lines: 160 Message-ID: References: MIME-Version: 1.0 Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Injection-Date: Wed, 22 May 2024 09:57:12 +0200 (CEST) Injection-Info: dont-email.me; posting-host="f7e0bc7db22343d0ab5efd8d30cb7c95"; logging-data="1153136"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX19mfYG9LstKrYax1rhscgWZ" User-Agent: Unison/2.2 Cancel-Lock: sha1:gbd3dJa741CBW9XvQjxFBx3m6i4= Bytes: 9328 On 2024-05-21 14:36:29 +0000, olcott said: > On 5/21/2024 3:05 AM, Mikko wrote: >> On 2024-05-20 17:48:40 +0000, olcott said: >> >>> On 5/20/2024 2:55 AM, Mikko wrote: >>>> On 2024-05-19 14:15:51 +0000, olcott said: >>>> >>>>> On 5/19/2024 9:03 AM, Mikko wrote: >>>>>> On 2024-05-19 13:41:56 +0000, olcott said: >>>>>> >>>>>>> On 5/19/2024 6:55 AM, Richard Damon wrote: >>>>>>>> On 5/18/24 11:47 PM, olcott wrote: >>>>>>>>> On 5/18/2024 6:04 PM, Richard Damon wrote: >>>>>>>>>> On 5/18/24 6:47 PM, olcott wrote: >>>>>>>>>>> On 5/18/2024 5:22 PM, Richard Damon wrote: >>>>>>>>>>>> On 5/18/24 4:00 PM, olcott wrote: >>>>>>>>>>>>> On 5/18/2024 2:57 PM, Richard Damon wrote: >>>>>>>>>>>>>> On 5/18/24 3:46 PM, olcott wrote: >>>>>>>>>>>>>>> On 5/18/2024 12:38 PM, Richard Damon wrote: >>>>>>>>>>>>>>>> On 5/18/24 1:26 PM, olcott wrote: >>>>>>>>>>>>>>>>> On 5/18/2024 11:56 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>> On 5/18/24 12:48 PM, olcott wrote: >>>>>>>>>>>>>>>>>>> On 5/18/2024 9:32 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>> On 5/18/24 10:15 AM, olcott wrote: >>>>>>>>>>>>>>>>>>>>> On 5/18/2024 7:43 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>>>>>>> No, your system contradicts itself. >>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>> You have never shown this. >>>>>>>>>>>>>>>>>>>>> The most you have shown is a lack of understanding of the >>>>>>>>>>>>>>>>>>>>> Truth Teller Paradox. >>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>> No, I have, but you don't understand the proof, it seems because you >>>>>>>>>>>>>>>>>>>> don't know what a "Truth Predicate" has been defined to be. >>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> My True(L,x) predicate is defined to return true or false for every >>>>>>>>>>>>>>>>>>> finite string x on the basis of the existence of a sequence of truth >>>>>>>>>>>>>>>>>>> preserving operations that derive x from >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> And thus, When True(L, p) established a sequence of truth preserving >>>>>>>>>>>>>>>>>> operations eminationg from ~True(L, p) by returning false, it >>>>>>>>>>>>>>>>>> contradicts itself. The problem is that True, in making an answer of >>>>>>>>>>>>>>>>>> false, has asserted that such a sequence exists. >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> On 5/13/2024 9:31 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>  > On 5/13/24 10:03 PM, olcott wrote: >>>>>>>>>>>>>>>>>  >> On 5/13/2024 7:29 PM, Richard Damon wrote: >>>>>>>>>>>>>>>>>  >>> >>>>>>>>>>>>>>>>>  >>> Remember, p defined as ~True(L, p) ... >>>>>>>>>>>>>>>>>  >> >>>>>>>>>>>>>>>>>  >> Can a sequence of true preserving operations applied >>>>>>>>>>>>>>>>>  >> to expressions that are stipulated to be true derive p? >>>>>>>>>>>>>>>>>  > No, so True(L, p) is false >>>>>>>>>>>>>>>>>  >> >>>>>>>>>>>>>>>>>  >> Can a sequence of true preserving operations applied >>>>>>>>>>>>>>>>>  >> to expressions that are stipulated to be true derive ~p? >>>>>>>>>>>>>>>>>  > >>>>>>>>>>>>>>>>>  > No, so False(L, p) is false, >>>>>>>>>>>>>>>>>  > >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> *To help you concentrate I repeated this* >>>>>>>>>>>>>>>>> The Liar Paradox and your formalized Liar Paradox both >>>>>>>>>>>>>>>>> contradict themselves that is why they must be screened >>>>>>>>>>>>>>>>> out as type mismatch error non-truth-bearers *BEFORE THAT OCCURS* >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> And the Truth Predicate isn't allowed to "filter" out expressions. >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> YOU ALREADY KNOW THAT IT DOESN'T >>>>>>>>>>>>>>> WE HAVE BEEN OVER THIS AGAIN AND AGAIN >>>>>>>>>>>>>>> THE FORMAL SYSTEM USES THE TRUE AND FALSE PREDICATE >>>>>>>>>>>>>>> TO FILTER OUT TYPE MISMATCH ERROR >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> The first thing that the formal system does with any >>>>>>>>>>>>>>> arbitrary finite string input is see if it is a Truth-bearer: >>>>>>>>>>>>>>> Truthbearer(L,x) ≡ (True(L,x) ∨ True(L,~x)) >>>>>>>>>>>>>> >>>>>>>>>>>>>> No, we can ask True(L, x) for any expression x and get an answer. >>>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> The system is designed so you can ask this, yet non-truth-bearers >>>>>>>>>>>>> are rejected before True(L, x) is allowed to be called. >>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>>> >>>>>>>>>>>> >>>>>>>>>>>> Not allowed. >>>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>>> My True(L,x) predicate is defined to return true or false for every >>>>>>>>>>> finite string x on the basis of the existence of a sequence of truth >>>>>>>>>>> preserving operations that derive x from >>>>>>>>>>> >>>>>>>>>>> A set of finite string semantic meanings that form an accurate >>>>>>>>>>> verbal model of the general knowledge of the actual world that >>>>>>>>>>> form a finite set of finite strings that are stipulated to have >>>>>>>>>>> the semantic value of Boolean true. >>>>>>>>>>> >>>>>>>>>>> *This is computable* Truthbearer(L,x) ≡ (True(L,x) ∨ True(L,~x)) >>>>>>>>>>> *This is computable* Truthbearer(L,x) ≡ (True(L,x) ∨ True(L,~x)) >>>>>>>>>>> *This is computable* Truthbearer(L,x) ≡ (True(L,x) ∨ True(L,~x)) >>>>>>>>>>> *This is computable* Truthbearer(L,x) ≡ (True(L,x) ∨ True(L,~x)) >>>>>>>>>>> *This is computable* Truthbearer(L,x) ≡ (True(L,x) ∨ True(L,~x)) >>>>>>>>>>> >>>>>>>>>>> >>>>>>>>>> >>>>>>>>>> So, for a statement x to be false, it says that there must be a >>>>>>>>>> sequence of truth perserving operations that derive ~x from, right? >>>>>>>>>> >>>>>>>>> Yes we must build from mutual agreement, good. >>>>>>>>> >>>>>>>>>> So do you still say that for p defined in L as ~True(L, p) that your >>>>>>>>>> definition will say that True(L, p) will return false? >>>>>>>>>> >>>>>>>>> >>>>>>>>> It is the perfectly isomorphic to this: >>>>>>>>> True(English, "This sentence is not true") >>>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>> Nope, Because "This sentece is not true" can be a non-truth-bearer, but >>>>>>>> by its definition, True(L, x) can not. >>>>>>>> >>>>>>> >>>>>>> True(L,x) is always a truth bearer. >>>>>>> when x is defined as True(L,x) then x is not a truth bearer. >>>>>> >>>>>> When x is defined as True(L,x) then x is what True(L,x) is, >>>>>> in this case a truth bearer. >>>> >>>>> This is known as the Truth Teller Paradox >>>> >>>> Doesn't matter. But ir you say that "x is not a truth bearer" then, >>>> by a truth preserving transformation, you imply that True(L,x) is >>> >>> True(English, "a cat is an animal) is true >>> LP := ~True(L, LP) expands to ~True(~True(~True(~True(...)))) >> >> No, it doesn't. It is a syntax error to have the same symbol on >> both sides ":=" so the expansion is not justified. > > ϕ(x) there is a sentence ψ such that S ⊢ ψ ↔ ϕ⟨ψ⟩. > *The sentence ψ is of course not self-referential in a strict sense*, > but mathematically it behaves like one. > https://plato.stanford.edu/entries/self-reference/#ConSemPar Your quote omitted important details. One is that the claim is not true about every theory but is about first order arithmetic and its extension. Another one is that ϕ(x) is that the claim is about every formula ϕ(x). > *That is great. That means that you agree with me using different words* Saying that you have a syntax error does not mean agreement. -- Mikko